Measurement uncertainty in a non-classical context

Diverse approaches to measurement uncertainty have been proposed as alternatives to well-established statistical methods. Some are founded on deductive inference systems that dismiss one law or another of classical logic, and purport processing of uncertainty in non-classical terms, e.g., fuzzy sets or belief measures. Intuitionistic logic, a deductive inference system where the law of excluded middle need not hold, is a case-study: since the logic of uncertainty is essentially inductive, a major point at issue is the viability of an intuitionistic probability calculus. An objective of this paper is to set the relevance of such a non-classical context to quantitative treatments of measurement uncertainty.